Abstract
In this paper we prove new identities in the Catalan triangle whose ( n , p ) entry is defined by B n , p : = p n ( 2 n n − p ) , n , p ∈ N , p ⩽ n . In fact, we show some new identities involving the well-known Catalan numbers, and specially the identity ∑ p = 1 i B n , p B n , n + p − i ( n + 2 p − i ) = ( n + 1 ) C n ( 2 ( n − 1 ) i − 1 ) , i ⩽ n , that appears in a problem related with the dynamical behavior of a family of iterative methods applied to quadratic polynomials.
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